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Daisuke Oyama and Satoru Takahashi
''Monotone and local potential maximizers in symmetric 3x3 supermodular games''
( 2009, Vol. 29 No.3 )
Generalized notions of potential maximizer, monotone potential maximizer (MP-maximizer) and local potential maximizer (LP-maximizer), are studied. It is known that 2x2 coordination games generically have a potential maximizer, while symmetric 4x4 supermodular games may have no MP- or LP-maximizer. This note considers the case inbetween, namely the class of (generic) symmetric 3x3 supermodular coordination games. This class of games are shown to always have a unique MP-maximizer, and its complete characterization is given. A nondegenerate example demonstrates that own-action quasiconcave supermodular games may have more than one LP-maximizers.
Keywords: equilibrium selection, supermodular game, monotone potential, MP-maximizer, local potential, LP-maximizer
Manuscript Received : Jul 09 2009 Manuscript Accepted : Aug 26 2009

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